Vibration analysis of planetary gearbox using empirical mode decomposition and automatic fault prediction using artificial neural network

Abstract

The planetary gearbox works on an epicyclic gear train consisting of sun gear meshed with planets gears and ring gear. It got advantages due to its large torque to weight ratio and reduced vibrations. It is mostly employed in analog clocks, automobile automatic gearbox, Lathe machines, and other heavy industries. Therefore, it was imperative to analyze the various faults occurring in a gearbox. Furthermore, come up with a method so that failures can be avoided at the early stage. It was also a reason why it became the field of intensive research. Moreover, the technology of neural networks emerged recently, where machine learning models are trained to detect uneven vibrations on their own. This attracted many researchers to perform the study to devise their own methods of prediction. The central concept of fault prediction by the neural network without human beings’ interference inspired this study. Most industries always wanted to know if their operation line is working fine or not. In this study, an attempt was made to apply the method of deep learning on one of the most critical gearboxes because of its components and functionality. A significant part of the study also involved filtering the vibration data obtained while testing. Comparative analysis of the variation of the peak of acceleration was performed for healthy and faulty conditions.

Keywords

Planetary gearbox neural networks deep learning

1 Introduction

Fault detection is an area of interest for many researchers. Given the development of deep learning techniques, researchers put more effort into using deep learning for automatic detection. These learning techniques always depend upon the data that is fed to them for training. However, it is always challenging to extract useful data from the gearbox, which could train neural networks. In this study, we used Empirical Mode Decomposition, one of the most efficient methods for filtering the data. The necessary features were extracted efficiently in the form of Intrinsic Mode Functions (IMFs). This field involving filtering of data and feeding it to a neural network is still in its initial phase. Less amount of studies are performed in the same field. The subsequent work is an attempt to reduce this gap by performing a practical experiment on the planetary gearbox to validate the result.

In this study, the Planetary gearbox is taken for inducing faults and collecting data as it is one of the most commonly used gearboxes in critical components. Its failure results in a large-scale catastrophe and loss of money. Therefore it is also vital for the industries to be equipped with a mechanism that predicts the failure accurately at an early stage. So that necessary measures are taken to prevent losses. GUO et al. (2011) discusses various applications of the planetary gearbox in his paper [8]. He mentions that the working condition of gearboxes is critical if the pattern and type of fault are to be determined, which is further cited in detail by SHARMA et al. (2016) [15]. In industries, the gearbox operates in rough conditions and is subjected to damages like fatigue crack, pitting, scaling. It is very much essential to devise fault diagnostic techniques so that faults are prevented.

MEHRABI (2013) mentions the main reason for the gearbox’s failure in his paper [13]. Once the power trains’ vibration frequencies add up and match with the natural frequency, it leads to resonance conditions failing. He further investigates the vibration modes and natural frequency of planetary gearbox in the same paper to avoid power train resonance. The significant outcome is that the stiffness on the natural frequency dominates the mass component. FERNANDEZ et al. (2015) perform a similar study [6] where he introduces an improved model for examining the results of faults like pitting and cracks on the meshing stiffness and load sharing ratio. Gear mesh frequency and its harmonics are the governing criteria for the gears’ vibrations as the varying stiffness occurs in the meshing process.

Some studies involve the methods of denoising the vibration obtained from the gearbox.

CHEN et al. (2013) propose a technique known as adaptive redundant multi-wavelet (ARM) to de-noise the received signal and convert it to a useful signal [4]. He also cites various other decomposition methods like empirical mode decomposition (EMD). MAHESHWARI et al. (2014) [12] introduces Hilbert Spectrum for domain transformation. His work also explains how EMD converts the raw, noisy signal into various functions known as Intrinsic Mode-Functions (IMFs). The Hilbert-spectral analysis processes the resulting data, which gives frequency information extracted from time-domain data.

Studies [1] and [2] are done to utilize the filtered data as well. In one of them, NARENDIRANATH BABU et al. (2017) investigates fault detection in journal bearings utilizing Daubechies Wavelet from data. He collects the vibration data using an accelerometer placed on the bearing, which is further decomposed using a wavelet transform. He uses Fast Fourier transformation to extract the frequency domain information from the signal in the time domain, giving the frequency peak amplitude. LIU et al. (2018) performs a similar study [11] and proposes a method for extracting features. He then performs diagnosis of fault using the same features for planetary gearbox using Variation Mode-Decomposition (VMD) for processing signal and Convolutional Neural-Network (CNN) for classifying faults. The significant outcome is that the vibration signal of an epicyclic gear transmission has a very intense noise. Therefore, it has to be decomposed using EMD or VMD., which is also one of the main reasons why EMD is chosen to filter the vibration data in the subsequent study.

It is also significant to obtain various features from the vibration data to determine the learning model’s accuracy. Therefore studies are done to get the hidden information by transforming the signal domain. ZIMROZ et al. (2011) proposes the research study [16], where he performs the extraction of hidden information in vibration signals by amplitude and frequency demodulators for the planetary stage. It becomes very useful when the machine works under non-stationary cyclic operations. It needs separate processing for signal and corresponding pattern recognition, suitable for time-varying systems. LIN et al. (2016) carry a similar study in which he observes the decrease in surface imperfections with technology advancements. These advancements result in frequency increasing more than 20 KHz. Therefore, it is necessary to study the nature of frequency domain data of vibration. Therefore frequency features are extracted from time-domain data obtained after transformation.

Speech is one of the most significant signals that is easily obtained for processing and determining the filtering method’s efficiency. On the contrary, extracting vibration data from mechanical components like gearbox requires more effort. CHAUDHARI et al. (2016) perform a study on speech signal enhancement, thus extracting the intrinsic mode function of EMD after Hilbert Huang’s transformation. He concludes that decomposing nonlinear and non-stationary signals should be done with EMD.

As this study involves using a planetary gearbox, it is essential to know the nature of vibration characteristics in the planetary gearbox. MIAO et al. (2015) perform a study [14] to understand the nature of vibration characteristics occurring during the planetary gearbox working with a single-stage. He also develops a diagnosis method to predict the fault in the gearbox based on characteristics. NARENDIRANATH BABU et al. (2018) also works [1] and [2] on the automatic fault classification of Journal bearing utilizing MATLAB tools. Both time domain, as well as frequency domain features are utilized in the input matrix. He also describes the Artificial Neural Network’s advantages over other prediction algorithms like CNN and DNN. Artificial Neural networks contain multiple layers of neurons (or perceptrons). The feeding of data is performed in a forward way. The CNN and DNN always deal with the information which requires processing at multiple layers; This is further used to extract features that neural networks can use to optimize the weights. As a result, it is mostly used to classify the images and 3 D models, which have the information distributed in 2 D or 3 D array/matrix. As the raw vibration data extracted from the gearbox is already processed to obtain features in their fine nature and are also in a single dimension, ANN is preferred for detecting faults in the gearbox.

The training of neural networks requires features to make decisions. Therefore, it is also equally important to understand what features must be extracted from filtered data. FU et al. (2015) work on features that can be useful for training the neural network [7]. He also uses a new method for fault diagnosis in roller bearing using adaptive C- means fuzzy clustering. He collects data using sensors and analyses. Nine-time domain features are extracted from the data. Five features are selected out of the nine features that form a new Eigenvector clustered for a more optimal solution.

The final part of the study involves the heavy use of deep learning, which is a branch of machine learning. It is composed of many layers for processing the data and learning from the patterns hidden in it. It uses a backpropagation algorithm to change the machine’s internal parameters for the representation of data in each layer. This concept finds a wide application in visual object recognition, speech recognition, audio, and video processing. KATHAIT et al. (2018) mention the application of image processing and convolution networks in intelligent character recognition (ICR) [9]. He also concludes that the efficiency of the tool can be increased by increasing the size of the training data set used to train the model. LECUN et al. (2015) discuss deep learning in detail in their paper [10].

The study performed carries two main objectives. The first one is the processing and filtering of raw vibration data using Empirical Mode-Decomposition to obtain the data free from unwanted noise. The resultant data is to be converted in the form from which features can be extracted easily. The second is to design the Artificial Neural Network and train it based on the features extracted. The trained model is further able to detect the faults induced in the planetary gearbox.

2 Experimental setup

The planetary gearbox’s vibration data was collected with the help of an accelerometer mounted on its top. The apparatus included a 1 HP motor with a diameter of 21 mm, which operated at 1440 rpm. it also included a 4:1 reduction planetary gearbox, a muff coupling to couple gearbox to motor. Wooden fixtures were used for the mounting of the equipment. Rubber paddings were put between the fixtures and gearbox base to damp extra vibrations and noise. The apparatus can be seen in the following Fig. 1.

Fig. 1

Experimental Apparatus containing Planetary Gearbox Coupled with a motor mounted on the wooden fixture.

3 Experimental procedure

Once the apparatus was prepared, four faults were induced in the planetary gearbox, and vibration data for the same along with healthy conditions was collected using a magnetic base accelerometer. Various positions were tested to find where the maximum amplitude of acceleration occurs so that accurate data could be stored. Accordingly, the accelerometer was mounted at that position. All the data were collected at a shaft speed of 1440 rpm without any external load applied to the gearbox. Vibration data was gathered for 1 minute at three different positions on the gearbox.

A data acquisition system (DAS) using 8702B50 type magnetic base accelerometer was used to collect the raw vibration data. DWESOFT software was used which processed the vibration data obtained by the accelerometer. It gave the plot of the amplitude of vibration versus time. which was further filtered utilizing empirical mode-decomposition. And subsequently, Fast-Fourier transformation was employed to provide the frequency domain data. The feature extracted from the time domain and frequency domain data was used to classify faults automatically using ANN. The different conditions of the gearbox considered for the fault classification are shown below figures.

The first reading was taken keeping gearbox healthy, as shown in Fig. 2a. No faults were induced in this condition, and gears were sufficiently lubricated.

Fig. 2a

Healthy Planetary Gearbox with sufficient lubrication.

The first fault was induced by putting a cut on the teeth on planet gear using EDM (Electric Discharge Machine), as shown in Fig. 2b. The second fault was induced by removing half teeth from the planet gear, as shown in Fig. 2c. The third fault was induced by removing three fourth teeth from the planet gear, as shown in Fig. 2d. The fourth fault was induced by adding 2 grams of dust in the casing of the gearbox, as shown in Fig. 2e.

Fig. 2b

Planetary gearbox with fault 1 induced.

Fig. 2c

Planetary gearbox with fault 2 induced.

Fig. 2d

Planetary Gearbox with fault 3 induced.

Fig. 2e

Planetary Gearbox with fault 4 induced.

4 Methodology

4.1 Empirical mode decomposition (EMD)

EMD is one of the methods of breaking down a raw signal without changing its domain. This method carries a very high value for analyzing non-linear and non-stationary signals. Natural vibration is an example of such a signal which contains a lot of noise.

EMD takes the raw signal as input and filters out the functions known as Intrinsic Mode Functions, which form a complete and nearly orthogonal basis for the original raw signal containing important information. Intrinsic Mode Functions (IMFs) are not necessarily in orthogonal form, but they are sufficient to describe the signal.

The IMFs obtained from EMD are very important to extract features from raw natural signals that contain a lot of noise. Since the filtering process does not allow its domain to change due to which the information related to frequency does not get lost. Once the noise is canceled out, the IMFs are easily used to extract the features we require to train the machine learning model. Obtaining IMFs from real-world gearbox vibration data is important because vibrations originate from multiple causes such as rotation of bearing, shaft, and gears’ meshing. Each of these causes may happen at specific time intervals. This type of data is very much evident in an EMD analysis but quite hidden in the other methods of filters.

The vibration data obtained during the experimentation was in the form of a non-stationary and nonlinear processing series. EMD method was used to decompose the raw signal into various modes function known as Intrinsic Mode-Functions. Also, frequencies at various times were obtained with high resolution. The resulting IMFs were in the time domain only and were free of noise. Therefore they were easy to process further for domain transformation using Fourier Transformation.

The following algorithm was used for performing the empirical mode decomposition of the experimentally obtained data:

Five seconds of original signal was taken

All local minima and maxima were extracted from and form respective lower and upper envelope using cubic interpolation.

The mean function was obtained for both upper as well as lower envelope and named it as M(t).

This average function M(t) is then subtracted from the original signal in order to obtain a new signal called y1(t).

Then, following two IMF conditions are checked for y1(t)–(a) the difference between the number of maxima/minima and number of zero crossings must be either zero or one and (b) the local average of the envelopes must be zero.

If above conditions are matched, y(t) is replaced with the residual, IMF{1}(t), where IMF{1}(t) = y(t) - y1(t).

If the above condition is not satisfied, y(t) is replaced by y1(t).

The above conditions are repeated until we receive a monotonic residual.

The vibration signal data of the gear box in the healthy condition and for each of the four different fault conditions are collected. The initial 5 %data for each second are collected and stored as a two-dimensional array. The initial step comprises extracting the time domain and time-frequency domain features through EMD. Feature extraction is mainly employed to assess the gear box performance degradation over time. An increase in gear box degradation is indicated by an increase in the magnitude of time domain features. Time domain features include eight classical features –RMS, kurtosis, skewness, peak to peak, crest factor, shape factor, impulse factor, margin factor –and two new features –add factor 1 and add factor 2. These two new features are used to link different features together. All these ten factors are summarised in Equations (6) to (13). In the equations, the initial value is calculated as the average of RMS of the healthy gear box.

Other than the ten time domain features obtained above, EMD is used to extract a set of new features called time-frequency domain values to make up for a more reliable database of features. Here, the gear box vibration signal is decomposed into characteristic IMFs. In the study, only the first seven IMFs are considered. The total energy of all the IMFs are calculated using Equation (14).

In the view of the powerful capability of Empirical Mode Decomposition (EMD) to process nonlinear or non-stationary signals, its algorithm efficiency and its satisfactory performance in minimizing energy leakage, the EMD is used in this paper to analyze the problem. The signals investigated are adaptively decomposed into a finite number of intrinsic mode functions (IMFs). The principal IMF’s, identified using an energy-distribution threshold, govern the signals oscillation. Therefore, the purified gear box vibration signals can be reconstructed from these principal IMFs. In order to remove interference present in principal IMFs, an adaptive band-pass filter is designed, whose central frequency is automatically set to the frequency dominating the IMF being investigated.

The novelty of this approach is that the EMD provides an adaptive, effective, and efficient way to obtain purified gear box vibration signals, which describe the transient gearbox vibration more vividly and precisely, reducing misinterpretation of the machine running condition.

Based on EMD practice, First, identifying the local extrema and construct two functions called the upper envelope and lower envelope by interpolating the local maxima and local minima, respectively. Next, taking their average; this produces a vibration signal of a gear box with a frequency lower than that of the original signal because the main pattern of the signal is confined between the two envelopes. Finally, by subtracting the envelope mean from x, the highly oscillatory wave is separated. Thus the filtering of the vibration signal in the gear box is achieved using EMD technique which is useful in industries to diagnose the faults at an early stage.

4.2 Fast fourier transformation (FFT)

Once the IMFs (Intrinsic Mode Function) were obtained as a result of Empirical Mode Decomposition, which was already in the time domain, these IMFs were converted into the frequency domain to obtain the instantaneous frequency. As a result, the complex signal was converted into a simpler form which facilitates analysis. The fast Fourier tool available in MATLAB was used to perform FFT on IMF and obtain frequency domain data. The peaks were determined in the frequency domain data to understand the, gearbox’s failing nature, and hence the type of failure was predicted. Two types of Fourier transform were used, which depends on the nature of input data.

Discrete Time Fourier Transform (DTFT): $X (e^{j ω}) = \sum_{n = - \infty}^{+ \infty} x [n] e^{- j ω n}$ (1) $x [n] = \frac{1}{2 π} \int_{- 2 π}^{+ 2 π} X (e^{j ω}) e^{j ω n} d ω$ (2)

Continuous Time Fourier Transform: $F (j ω) = \int_{- \infty}^{+ \infty} f (t) e^{- j ω t} dt$ (3) $f (t) = \int_{- \infty}^{+ \infty} F (j ω) e^{j ω t} d ω$ (4)

4.3 Gear train mesh frequency

It is referred to the frequency at which the two gears mate with each other. It depends on the teeth number of gear and its speed. The sensor is placed in a position where maximum vibration is obtained, and in doing so, the gear mesh frequency is obtained as gear mesh frequency only results at the position of maximum vibration in the gearbox. Also, when the planet gear revolutes completely relative to the sun gear, the Number of meshed teeth with sun gear is the same as with ring gear. Therefore, the Gear Train Mesh frequency of sun gear meshed with planet gear is the same as the planet gear meshed with the ring gear. The relation for calculating the gear train mesh frequency for the single-stage planetary gearbox is given as $f_{m} = f_{h} \times z_{r} = \frac{z_{r} z_{s}}{z_{r} + z_{s}} \times f_{s}$ (5)

Where f_m = Gear meshing frequency $\begin{matrix} f_{h} = Relative rotating frequency \\ z_{r} = Number of teeth of ring gear \\ z_{s} = Number of teeth of sun gear \\ f_{s} = sun gear speed \end{matrix}$

4.3.1 Calculation of gear mesh for healthy data

For planetary gearbox used for the study, following are the parameters obtained $\begin{matrix} Number of teeth of ring gear z_{r} = 104 \\ Number of teeth of sun gear z_{s} = 26 \end{matrix}$

Gear Ratio = 4:1

RPM of sun gear = 1440/4 = 360

ω_s = (360×2π)/60

F_s =ω_s/2π

⟶ F_s = 6 Hz

Gear meshing frequency F_m = (104×26×6)/(104 + 26) = 124.8 Hz

4.4 Automatic fault classification using Artificial Neural Network (ANN)

Neural pattern recognition tool in MATLAB was used for the automatic classification of faults. The vibration data was divided into four equal parts of five seconds for all five conditions of the gearbox. So a total of 20 samples were generated. Feature extraction was used for extracting time domain as well as frequency domain features. The decrease in the working condition of the gearbox was indicated by the increase in the amplitude of features of the time domain.

Following seven features of time-domain were used as an input in neural pattern recognition tool (npr tool) in MATLAB: Mean, Variance, RMS, Median, Kurtosis, Skewness, Standard deviation.

Along with time-domain features, the following two frequency domain features were extracted from filtered data for neural processing:

Peaks, Energy of frequency spectrum.

Therefore the input matrix size was 20×9. The 20 samples were extracted from the gearbox subjected to five different conditions. Therefore the output was linked to a 20×5 matrix. The training was done using the scaled conjugate method with ten hidden neurons. 70%data was employed for training, 15%data was employed for the testing, and 15%of remaining input data was employed for validation. The confusion matrix, performance diagram, Receiver operating characteristic plot, and error histogram were plotted for the same. Various time domain features are given below. $\underline{X} = \frac{1}{n} \sum_{i = 1}^{n} | x_{i} |$ (6) $X_{median} = \frac{\frac{n}{2} - cf}{f} (w) + L_{m}$ (7) $SD = \sqrt{\frac{\sum {| x - \underline{x} |}^{2}}{n}}$ (8) $X_{var} = \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \underline{X})}^{2}$ (9) $X_{RMS} = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} x_{i}^{2}}$ (10) $X_{kur} = \frac{1}{n} \frac{\sum_{i = 1}^{n} x_{i}^{4}}{X_{RMS}^{4}}$ (11) $X_{P} = \frac{1}{n} \sum_{i = 1}^{n} X_{pi}$ (12) $X_{skew} = E [{(\frac{x - μ}{σ})}^{3}]$ (13) $E = \sum_{i = 1}^{n} Ei$ (14)

5 Results and discussion

5.1 Collection of vibration data with various induced faults:

The vibration data for the four faults induced in a single-stage 4:1 reduction planetary gearbox was utilized for processing. Using the MATLAB code, Empirical Mode-Decomposition was performed on the obtained data, and various mode functions known as intrinsic mode-functions were obtained. As the mode functions obtained were in the same domain but with less noise, it became quite useful to obtain peaks that correspond to the feature information required for the training of Artificial Neural Network. The method of EMD always carries a very high value for analyzing non-linear and non-stationary signals as a result of which it was used for the filtering vibration related to our planetary gears, which contained a different type of noises because of the bearing and shaft rotations. Also we needed more features for the training of the model which were obtained by the frequency domain graphs of the same filtered data. In order to convert the mode functions of time domain to frequency domain we used the Fast Fourier Transformation which was applied to eighth IMF.

5.1.1 Planetary gearbox at healthy condition:

This condition corresponds to the normal condition at which the gearbox was operated with sufficient lubrication and no-fault. As the conditions were normal, therefore vibrations obtained were of very small amplitudes as compared to other conditions. Figure 3a shows the original time-domain signal of a healthy gearbox. Figure 3b shows Intrinsic Mode-Functions (IMFs) obtained after performing EMD of the original time-domain signal. From Fig. 3c, a peak amplitude of 0.06403 m/s2 and frequency of 124.8 Hz is observed which is less than the raw signal frequency domain.(148.2 Hz)

Fig. 3

a) Original time domain signal, b) Frequency domain signal obtained by applying Fast-Fourier Transform on raw time domain signal. c) Intrinsic Mode-Functions (IMFs) obtained after performing EMD of original time domain signal d) Frequency domain signal obtained by applying Fast-Fourier Transform on 8th IMF.

5.1.2 Planetary gearbox at fault 1 condition:

This condition corresponds to the first fault condition in which the cut of depth 1 mm was put on the planet gear using EDM, resulting in less contact of teeth, causing noise and vibrations. As the operating conditions were not normal, therefore vibrations obtained were having slightly higher amplitudes than the healthy condition. Figure 4a shows original time domain signal for fault 1 condition.

Fig. 4

a) Original time domain signal, b) Frequency domain signal obtained by applying Fast-Fourier Transform on raw time domain signal, c) Intrinsic Mode-Functions (IMFs) obtained after performing EMD of original time domain signal d) Frequency domain signal obtained by applying Fast-Fourier Transform on 8th IMF.

Figure 4b shows Intrinsic Mode Functions (IMFs) obtained after performing EMD of original time domain signal. From Fig. 4c, peak amplitude of 0.07326 m/s2 and frequency of 124.2 Hz are observed which is again less than one observed from raw time domain signal where prequency peak obtained was 147.8 Hz

5.1.3 Planetary gearbox at fault 2 condition:

This condition corresponds to the second fault condition in which half of the teeth of planet gear were removed using an EDM to replicate light wear out of teeth which caused due to interference and improper lubrication. Since the contact surface was reduced, more vibration and noise was getting produced, leading to less transmission of torque and more disturbance in the gearbox. Figure 5a shows original time domain signal for fault 2. Figure 5b shows Intrinsic Mode Functions (IMFs) obtained after performing EMD of original time domain signal. From Fig. 5c, peak amplitude of 0.1566 m/s2 and frequency of 149 Hz are observed. Figure 5a

Fig. 5

5.1.4 Planetary gearbox at Fault 3 condition:

This condition corresponds to the third fault condition in which three fourth teeth of planet gear were removed using an EDM to replicate immense wear out of the teeth caused in the case of interference. Therefore, as a result, the vibration and noise increased with respect to earlier faults. 6a shows original time domain signal for fault 3 condition. Figure 6b shows Intrinsic Mode Functions (IMFs) obtained after performing EMD of original time domain signal. From Fig. 6c, peak amplitude of 0.3382 m/s2 and frequency of 172.8 Hz are observed. It also resulted in the temperature rise of the gearbox.

Fig. 6

5.1.5 Planetary gearbox at fault 4 condition:

This condition corresponds to the fourth fault condition in which 2 grams of dust was added to replicate the fault that gets induced in a particular gearbox, which is maintained frequently by disassembling and assembling again, resulting in contamination of lubricant and causing the problem. Fig. 7a shows the original time-domain signal for the fault 4 conditions. Figure 7b shows Intrinsic Mode Functions (IMFs) obtained after performing EMD of the original time-domain signal. From Fig. 7c, the peak amplitude of 0.3785 m/s2 and frequency of 148.2 Hz is observed

Fig. 7

a) Original time domain signal, b)) Frequency domain signal obtained by applying Fast-Fourier Transform on raw time domain signal c) Intrinsic Mode-Functions (IMFs) obtained after performing EMD of original time domain signal d) Frequency domain signal obtained by applying Fast-Fourier Transform on 8th IMF.

5.1.6 Summary of above results

Experimental gear mesh frequency obtained was 124.8 Hz which was close to theoretical gear mesh frequency obtained that is 105.6 Hz, Hence the results are validated.

The EMD method is able to give more precise results as compared to the conventional fast Fourier transform and wavelet transforms. One advantage lies in the ability of EMD method is to process non-linear and non-stationary signals. Another advantage is the capability to monitor real time data from gear box which helps to predict defects before failure, hence improving the running time of machines. The major advantage of the empirical mode decomposition lies in the fact that various frequency ranges can be analysed by this method to pin point the fault. This proves helpful in various industries where a large amount of vibration data, may be for days, needs to be analysed.

The FFT power spectrums indicated that the frequency of peaks at BF (Bearing Frequency) for healthy and various defect conditions. It is clear that the FFT represent considerable increase in frequency compared to EMD spectrums. However, the increase in frequency at BF as obtained from FFT spectrum is very maximum. From the FFT power spectrum, it is difficult to identify the faults.

The enveloped EMD technique is proved to be a valuable tool in conjunction with routine vibration data to provide a more complete picture of the health of the rotating machinery. Thus the condition monitoring provides more effective in early diagnosis of gear box faults. The results show that various fault vibration signals and the fault detection rate of the proposed method is more superior than that of FFT. Also, FFT is not good for non-periodic and non-stationary signals.

5.2 Automatic fault classification with the help of artificial neural networks (ANN)

Artificial Neural Network forms a base for deep learning, a sub-field of machine learning where the human brain’s structure inspires algorithms. It takes in data, trains based on the pattern found in it, and predicts the output for a similar data set.

An artificial Neural Network is made up of layers of neurons, which is a core processing unit of the network.

The basic architecture of artificial neural networks contains three layers, namely input, output, and hidden. Input layer takes the input. The output layer predicts the output. Hidden layer performs all kinds of computation required for the working of the network.

Table 1
Summary of Frequency and amplitude in different gearbox condition

Condition Frequency (Hz) Amplitude (m/s²)

Healthy 124.8 0.06403

Fault 1 124.2 0.07326

Fault 2 149 0.1566

Fault 3 172.8 0.3382

Fault 4 148.2 0.3785

Condition	Frequency (Hz)	Amplitude (m/s²)
Healthy	124.8	0.06403
Fault 1	124.2	0.07326
Fault 2	149	0.1566
Fault 3	172.8	0.3382
Fault 4	148.2	0.3785

The data value for each feature is sent to the neurons present in the input layer. The information passes on to the next layer through channels, and each of these channels is assigned some weights. Inputs are multiplied with corresponding weights and sent to the next hidden layer where some bias is added to all the neurons, and then the data is passed through the activation function, the result of which determines if the Neuron will get activated or not. The activated Neuron transmits data into the next hidden layer. This process of transmitting data in the forward direction is called forward propagation. The Neuron with the highest value determines the output in the output layer. The error is calculated on the basis of actual and predicted output, and this information is sent backward so that weights in the initial channel can be adjusted. This is called backpropagation. This iterative process keeps on happening until the predicted and actual output matches. Once that stage is reached, we can confirm that our model is trained to perform automatic classification for our gearbox’s faulty states.

Similarly ANN is used for our experiment where it is implemented on the healthy state of the gearbox and in faulty conditions. The training is done using a scaled conjugate method with 10 hidden neurons.7 time domain and 2 frequency domain features are extracted and given to the network as input. 70%of input data is implemented for training, 15%of input data is employed for testing, and 15%of remaining input data is employed for validation. The confusion matrix, performance diagram, receiver operating characteristics plot, error histogram, and training state performance are plotted for the same.9 different features, four different faults, and the healthy gearbox are given as inputs. The neural network training characteristics are shown in Fig. 8. The results are obtained after 35 iterations of the classification process, as can be seen from Fig. 8.

Fig. 8

Neural Network.

The various ANN parameters obtained were as follows.

a) Performance Graph

The network error drop is shown in the performance diagram in Fig. 9. The cross-entropy error function was used for validation. The decrement in the blue line signifies the decrement of error in training data. Similarly, the green line signifies validation error. The training was stopped when the validation error decreased. The red line shows an error in the test data. It is visible from the graph that the best validation error is at epoch 35, and therefore training stopped after 35 iterations.

Fig. 9

Performance Graph.

b) Training State Performance

It is evident from the graph in Fig. 10 that the data set was presented 35 times to the learning algorithm. The neural network carried out six validation checks. The validation failure at various epochs is presented in the graph.

Fig. 10

Training State Performance.

c) Receiver Operating Characteristics Plots

The performance of neural networks is also given by Receiver-Operating-Characteristic (ROC) (Fig. 11). ROC gave us a plot between true positive rate and false-positive rate. A good performance indicates that it should not cross the false-positive rate, and the area under the true positive rate should be more. Therefore, according to the figure, it was concluded that the method employed was good.

Fig. 11

Receiver Operating Characteristic Plots.

d) Error Histogram

Figure 12 shows the error histogram. The error histogram was given by dividing the errors into 20 bins. The orange line in the figure shows the zero error line. It is visible that error values were close to zero lines and were negative in value which implied that it was inversely correlated.

Fig. 12

Error Histogram.

Therefore the results were also validated. The 20 bins are very close to 0 and 1, which suggests the accuracy of the neural network.

e) Confusion Matrix

In this matrix, the whole dataset was used to form the matrix. The Rows indicate the predicted or the output classification, and respective columns indicate the targeted classification. The diagonal cells represent the samples that were predicted as well as classified correctly, and similarly, the cells which are not on diagonal represent the samples that were not correctly classified. The extreme columns and rows represent the total percentage of all the samples that were predicted to classify incorrect as well as incorrect classes. The data in the extreme column is known as correct prediction rate and false prediction rate, respectively. At the same time, the bottom-most row represents the total percentage of all those samples that were either classified into the correct or incorrect classes. This data in the row is known as recall rate. It can be a positive rate and a negative rate, respectively. The most-bottom point shows the overall accuracy of the results obtained. The result obtained had an accuracy of 100%. Similarly, for training, validation, and testing confusion matrices, the results have 100%accuracy.

The interpretation and performance of results are portrayed with the help of confusion matrix shown in Fig. 13 which shows how valid are results. It consists of four different matrices which are Training Matrix, Validation Matrix, Testing Matrix and an all confusion matrix.

Fig. 13

Confusion Matrix Summary.

6 Conclusion

Planetary gearbox finds a wide range of applications in industries. So real-time monitoring of the gearbox becomes a useful task to avoid its failure. The above study attempted to create a similar mechanism for real-time monitoring. Such mechanisms with automatic classification can help the industries locate the fault in the production line and avoid the unplanned plant shutdown caused due to failure of their critical machine components.

EMD has various advantages of its own like the ability to process irregular and non-stationary signals. It also has the ability to monitor real time data from planetary gearbox which helps to predict defects before failure, hence improving the running time of machines. Also Empirical Mode Decomposition is very helpful in analyzing data from various range of frequency and hence very much efficient in pin pointing the fault. This proves helpful in various industries where a large amount of vibration data, is required to be analyzed. The methodology of EMD helped in producing the filtered IMFs from intensely noised data. The IMFs contained more transparent information related to the vibration’s nature, which was extracted to create more distinguished feature values for different readings of faults. These distinguished feature values carry all the credit for the successful training of the Neural Network Model. It was proved that the efficiency of EMD to filter the data with intense noise becomes very helpful in developing the neural network with higher accuracy and classification rate. Fourier Transformations were also useful for obtaining the necessary frequency domain features apart from time-domain features, used to train neural networks. The hidden features extracted from the frequency domain provided the necessary information needed to optimize the neural network, hence increasing the accuracy in the prediction of the trained model. The trained model was capable of classifying any faulty condition under which the gearbox is operating. Even if the gearbox is not undergoing faulty vibrations, The model equipped with a proper user interface can be used to monitor the condition of the gearbox without human involvement. More future work can be done in the area dealing with preprocessing of data and changing the neural network model parameters to improve the accuracy and lower the losses.

In this study, EMD is used to extract certain other features known as time frequency domain features which are used to build a more reliable and robust database. Here, we obtain the EMD energy entropy of each IMF which varies with variation in energy of vibration signals. The advantage of the proposed method lies in the ability to handle real time data from gear box for condition monitoring and fault prediction. Since the confusion matrix allows visualisation of the performance of an algorithm, a supervised learning has good percentage of probability. Therefore this method can be concluded as a good one to process real time data due to prediction above 90%. Also the feature extraction scheme including time domain, frequency, and time frequency domain feature is superior to the single mode schemes.

The statistical features used are a powerful tool which characterises the change of gear box vibration signals when faults occur. The benefits of these features are the simplicity of implementation, low computational time and saves monetary costs to the industries. Figure 14 shows the roadmap for implementation of methodology.

Fig. 14

Roadmap for implementation of methodology.

Finally we concluded that Fourier analysis assumes that a signal is stationary and consists of components of a pure tone. In the gear box practice, the frequency information can evolve over larger time and several such frequencies can be compounded. The above EMD procedure is useful for identifying the amount of variation due to oscillation at different scale and time location and extracting an oscillatory wave from a nonstationary signal.

It is demonstrated that the proposed EMD technique provides a feasible and reliable way to interpret gear box vibration, by which means the machine condition can be diagnosed correctly. The proposal can be fit into existing frameworks as most of the industries already use DAQ (Data Acquisition Systems) to monitor their machineries. This means the sensors are placed on the machines to capture the vibration data. However, with this machine learning model which is pre trained to classify faults, the recorded data can be fed into it to determine the type of fault. The existing framework lack the capability of predicting the type fault which can be fulfilled by the use of machine learning model which are pre trained with similar data. Fault classification of gearbox using ANN is highly useful in industries in predicting faults at an early stage. So that the accidents and the plant shut can be avoided. This will save cost benefits to the industries.

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